Stars come in all different brightnesses and distances, which makes the sky very
ID: 3112532 • Letter: S
Question
Stars come in all different brightnesses and distances, which makes the sky very complicated in appearance. Two quantities determine how bright a star will appear in the sky. The first is its distance, and the second is the brilliance or ‘luminosity’ of the star, measured in watts. If you take a 100-watt light bulb and place it 10 meters away from you, the amount of light you see will look the same as a 1-watt light bulb only 1 meter away. For stars, the apparent brightness or ‘magnitude’ of a star depends on its distance and its luminosity, also called its absolute magnitude. What you see in the sky is the apparent brightness of a star. The actual amount of light produced by the surface of the star is its absolute magnitude. A simple equation, basic to all astronomy, relates the star’s distance in parsecs, D, apparent magnitude, m, and absolute magnitude, M as follows: M = m + 5 - 5log(D)
Problem 1 – The star Sirius has an apparent magnitude of m = -1.5, while Polaris has an apparent magnitude of m = +2.3. If the absolute magnitude of Sirius is M = +1.4 and Polaris is M = -4.6, what are the distances to these two stars?
Problem 2 – An astronomer determined the distance to the red supergiant Betelgeuse as 200 parsecs. If its apparent magnitude is m = +0.8, what is the absolute magnitude of this star?
Problem 3 – As seen in the sky, Regulus and Deneb have exactly the same apparent magnitudes of m = +1.3. If the distance to Deneb is 500 parsecs, and the absolute magnitude of Regulus is 1/9 that of Deneb, what is the distance to Regulus?
Explanation / Answer
1.For Sirius the equation will be, 1.4=-1.5+5-5log(D)
Or, -2.1=-5log(D)
So, D =antilog(2.1/5)
D = -0.37 parsec
For Polaris the equation is, -4.6=2.3+5-5log(D)
Or, -11.9=-5log(D)
So, D=antilog(11.9/5)
D=0.37 parsec
The appearence of the negative sign in the first result indicates the fact that both the stars will appear at diametrically opposite positions with respect to the observer.